Molecular characterization of poly(diisopropyl fumarate) by the absolute calibration method in molecular exclusion chromatography (GPC)

The present work demonstrates that it is possible to obtain the parameters K and a of the Staudinger-Mark-Houwink relationship between the intrinsic viscosity [η] and the molecular weight M of a polymer by applying the absolute method of exclusion chromatography to samples of poly (diisopropyl fumarate). The procedure is based on deducing the relationship between molecular weight and elution volume V from chromatographic runs of a stoichiometrically labeled polymer sample with a broad molecular weight distribution. By using double detection it is possible to obtain the relationship f(V)/h(V) = M(V)/M_n = exp (A-BV)/M_n where M_n is the osmotically determined number average of the molecular weight of the eluted polymer while f(V) and h(V) are the normalized elution curves obtained by the use of the polymer mass detector and the label detector respectively. A and B are the parameters of the calibration curve, i.e., the relationship between M and V which together with the intrinsic viscosity and the elution curves of several samples of the polymer allows us to obtain the relationship between [η] and M. The results have been verified with chromatographic data through the use of the universal calibration concept.     

1,2-聚丁二烯长链支化的研究

本文研究了1,2-结构含量在80～90%的1,2-聚丁二烯的长链支化,发现聚合物的立体规整性与聚合物的分子量无关,可以用GPC-自动粘度计联用技术研究其长链支化,产生支化的临界分子量为40万左右。     

用凝胶色谱与毛细管粘度计联用法研究顺丁胶的长链支化

本文讨论了用GPC与自动粘度计联用技术测定高聚物长链支化度的方法,将得到的实测关系[η](V)转化成校准关系[η](V_R)后,利用在同一淋出体积流出支化物和线型分子的([η]·M)乘积相等这一普遍原理,计算出各级分的支化因子g_i、总平均支化因子以及产生支化的临界分子量M~*,并讨论了检测器与粘度计连结管死体积△V及虹吸管残留液对支化参数计算值的影响。     

Gel permeation chromatography of polyethylene: Effect of long-chain branching

The effect of long-chain branching on the size of low-density polyethylene molecules in solution is demonstrated through solution viscosity and molecular weight measurements on fractionated samples. These well-characterized fractions are analyzed by gel permeation chromatography (GPC), and it is shown that the separation of the polymer molecules by this technique is sensitive to the presence of long-chain branching. By using fractions of branched polyethylene possessing differing degrees of branching, one observes that a single curve is adequate in relating elution volume to molecular weight. This calibration curve is applied in the GPC analysis of a variety of commercial low-density polyethylene resins and it is shown, by comparison with independent osmometric and gradient elution chromatographic data, that realistic values for molecular weight and molecular weight distribution are obtained. The replacement of molecular weight M by the parameter [η]M as a function of elution volume, leads to a single relationship for both linear and branched polyethylenes. This indicates that GPC separation takes place according to the hydrodynamic volumes of the polymer molecules. The comparison of data for polyethylene and polystyrene fractions suggests that this volume dependence of the separation will be observed for other polymer–solvent systems.     

Étude des systémes ternaires polymère-mélanges de solvants: relation entre solvatation préférentielle et viscosité

The preferential solvation of ternary systems of polymer with mixed solvents is characterized by the λ′ parameter which depends on the thermodynamic properties of the system and also on some molecular parameters of the polymer (molecular weight, index of polydispersity, index of branching etc.). The dependence of λ′ on molecular parameters can be illustrated by a unique relation between the λ′ parameter and the intrinsic viscosity [η]:λ′[η] = λ′_∝ [η] + a′ +. This representation is verified for polystyrene and polymethyl methacrylate in several mixed solvents.     

Intrinsic viscosity of polydisperse branched polymers

The relationships between molecular weight distribution and structure in polymerizations with long-chain branching were reviewed and extended. Results were applied to an experimental examination of intrinsic viscosity in polydisperse, trifunctionally branched systems. Several samples of poly(vinyl acetate) were prepared by bulk polymerization under conditions of very low radical concentration. The relative rate constants for monomer transfer, polymer transfer, and terminal double-bond polymerization were established from the variation of M _n and M _w with the extent of conversion. Average branching densities were then calculated for each sample and ranged as high as 1.5 branch points/molecule. Intrinsic viscosities [η]_B were measured in three systems: a theta-solvent, a good solvent, and one that was intermediate in solvent interaction. These results were compared with calculated viscosities, [η]_L, which would have been observed if all the molecules had been linear. The values of [η]_B/[η]_L were substantially the same in all three solvents. The variation of this ratio with branching density was compared with the theory of Zimm and Kilb as adapted to polydisperse systems. Discrepancies were noted, and the adequacy of present model distribution functions for branched polymers was questioned.     

Well-Defined Aminophenolate Zinc and Magnesium Complexes as Excellent Inhitiators for the ROP of Lactides

A series of molecular homo and heteroleptic zinc and magnesium compounds with aminophenolate ligands [(µ,η²-L²)ZnEt]₂ ( 1 ), [(η²-L²)Zn(µ-BnO)]₂ ( 2 ), [Zn(η²-L²)₂] ( 3 ), [Zn(η²-L³)₂] ( 4 ), [Mg(η²-L³)₂] ( 5 ) (L²-H = N-[methylene(2-hydroxy-3,5-di-tert-butylphenyl)]-N-methyl-N-cyclohexylamine, L³-H = N-[methylene(2-hydroxy-3,5-di-tert-butylphenyl)]-N-methyl-N-methyl-1,3-dioxolaneamine) have been prepared and characterized. The homoleptic complexes 3–5 are most probably a mixture of diastereoisomers that in solution show an interesting dynamics which plays an important role in their catalytic behavior. The complexes 2 – 5 are efficient initiators in ring-opening polymerization (ROP) of lactides to produce polymers with desired molecular weight and narrow polydispersity.     

Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Determination of polymer branching with gel-permeation chromatography. II. Experimental results for polyethylene

The recently developed methods of characterizing branching in polymers from gelpermeation chromatography and intrinsic viscosity data are verified experimentally. An iterative computer program was written to calculate the degree of branching in whole polymers. Long-chain branching in several low-density polyethylene samples was determined by both the fraction and whole polymer methods. The two methods gave consistent ranking of the branching in the samples although absolute branching indices differed. Effects of various experimental errors and the particular model used for branching were investigated. For polyethylene, the data show that the effect of branching on intrinsic viscosity is best described by the relation 〈g₃〉_W^1/2 = [η]_br/[η]₁ where 〈g₃〉_w is the weight-average ratio of mean-square molecular radii of gyration of linear and trifunctionally branched polymers of the same weight-average molecular weight.     

Size Exclusion Chromatography of Poly(vinylpyrrolidone)

Abstract

Poly(vinylpyrrolidone) and poly(ethylene oxide) separate by hydrodynamic volume on Toyo Soda TSK-PW columns in a mixed solvent mobile phase of 50:50 (v/v) MeOH/H₂O containing 0.1M LiNO₃. From this separation a single universal calibration curve based on hydrodynamic volume [η]M can be obtained. Accurate weight average molecular weights of PVP were obtained by both SEC/LALLS and universal calibration showing good agreement between the two methods. SEC/LALLS overestimates the number average molecular weight for broad distribution polymers due largely to the lack of sensitivity of the LALLS detector to the low molecular weight portion of the polymers, while the universal calibration method slightly underestimates the number average molecular weight as compared to osmometric values.     

Separation of dextrans by gel permeation chromatography

The role of the intrinsic viscosity [η] as separation parameter in gel permeation chromatography (GPC) was studied for dextrans (from Leuconostoc mesenteroids B512) dissolved in water with deactivated silicagel (Porasil) as the column-filling material. For that purpose specific viscosities of dextran fractions eluted by GPC were measured as a function of the elution volume v. Provided that the elution volumes are corrected for zonal spreading, they are related to the intrinsic viscosities in an unambiguous way, probably reflecting a unique relationship between degree of branching and molecular weights. This was further investigated by developing an iteration method to prepare two calibration curves γ(v) and g(v), respectively, relating ln[\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}] and InM (M is the molecular weight) to v. It required that the weight-average molecular weight M _w, the number-average molecular weight M _n, and the average intrinsic viscosity [\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}] for a number of dextran samples (broad distributions) be previously known. The calibration curves found lead to consistent values of the above-mentioned averages. Moreover, they allow-establishment of the [\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}]-M relationship over the range 5000 < M < 500,000.     

Determination of molecular weight distribution of cellulose by conversion into tricarbanilate and fractionation

Two samples of cellulose (molecular weight 2.97 × 10⁵ and 1.25 × 10⁵) were transformed into carbanilates (CTC) which were then fractionated by the elution method at a constant composition of the acetone-water elution mixture with the column temperature gradually increasing from ?30°C to 30°C, and by the GPC method in acetone and tetrahydrofuran. Tetrahydrofuran appeared to be a more suitable solvent. The molecular weights of fractions obtained by the elution fractionation were determined by the light-scattering method in tetrahydrofuran. The width of fractions was determined by the GPC method (average M _w/M _n = 1.37); the [η] values and the Mark-Houwink constants (K = 5.3 × 10^-3, a = 0.84) for tetrahydrofuran at 25°C were determined. The calibration curve for the GP method was constructed by means of the fractions thus obtained; it was demonstrated that the universal calibration curve according to Benoit can also be used. It was demonstrated that the molecular weight distribution of cellulose can be conveniently determined by conversion into CTC followed either by the elution fractionation (for preparative purposes) or by fractionation by the GPC method (for analytical purposes).     

Universal Calibration and Molecular Weight Averages in Gel Permeation Chromatography Illustrated by Cellulose Nitrate and Poly(oxypropylene)

Abstract

The nature of the averaging process in the analysis of gel permeation chromatograms was examined for cases where the molecules in the detector cell of the apparatus were of different molecular weight and of the same molecular weight. When the molecules have the same molecular weight, the hydrodynamic volume (1), [?]M, averaged across a chromatogram was found to become KM^a+1 for any molecular weight average at the elution volume corresponding to that average. [η] is intrinsic viscosity, M is molecular weight, and K and a are the appropriate Mark-Houwink constants. Thus when size separation is by molecular weight, the universal GPC calibration functions include KM_n ^a+1 where M_n is the number average molecular weight.

Cellulose nitrate and poly(oxypropylene) were analyzed using three sets of columns and two GPC instruments. KM_n ^a+1, KM_w ^a+1, and [η]M_w were found to represent the hydrodynamic volume since these functions fell on the universal calibration plot for nearly nono-disperse polystyrene standards. The function [η]M_n was displaced from the polystyrene universal calibration plot by factor which equaled M_w/M_n. The slopes and intercepts of the universal calibration plots were found to be completely consistent with the slopes and intercepts of the molecular weight calibration plots showing that the Mark-Houwink constants were correct. Intrinsic viscosity - molecular weight relations were presented for 12.0–12.6%N cellulose nitrate and for low molecular weight poly(oxypropylene), the latter relation being a correction of that of Sholtan and Lie (18).     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Poly(2,6-diphenyl-1,4-phenyl oxide): Characterization by gel-permeation chromatography,light scattering,and solution viscosity

Ten unfractionated poly(2,6-diphenyl-1,4-phenylene oxide) samples were examined by gel permeation chromatography (GPC) and intrinsic viscosity [η] at 50°C in benzene, by intrinsic viscosity at 25°C in chloroform, and by light scattering at 30°C in chloroform. The GPC column was calibrated with ten narrow-distribution polystyrenes and styrene monomer to yield a “universal” relation of log ([η]M) versus elution volume. GPC-average molecular weights, defined as M?gpc = \documentclass{article}\pagestyle{empty}\begin{document}$\Sigma w_i [\eta ]_i M_i /\Sigma w_i [\eta ]_i$\end{document}, w_i denoting the weight fraction of polymer of molecular weight M_i, were computed from the GPC and [η] data on the polyethers. The M?GPC were then compared with the weight-average M?_w from light scattering. The intrinsic viscosity (dl/g) versus molecular weight relations for the unfractionated poly(2,6-diphenyl-1,4-phenylene oxides) determined over the molecular weight range 14,000 ≤ M?_w ≤ 1,145,000 are log [η] = ?3.494 + 0.609 log M?_w (chloroform, 25°C) and log [η] = ?3.705 + 0.638 log M?_w (benzene, 50°C). The M?_w(GPC)/M?_n(GPC) ratios for the polymers in the molecular weight range 14,000 ≤ M?_w ≤ 123,000 approximate 1.5 according to computer integrations of the GPC curves with the use of the “universal” calibration and the measured log [η] versus log M?_w relation. The higher molecular weight polymers (326,000 ≤ M?_w ≤ 1,145,000) show slightly broadened distributions.     

Influence of the catalyst and polymerization conditions on the long‐chain branching of metallocene‐catalyzed polyethenes

A study was made on the effects of polymerization conditions on the long‐chain branching, molecular weight, and end‐group types of polyethene produced with the metallocene‐catalyst systems Et[Ind]₂ZrCl₂/MAO, Et[IndH₄]₂ZrCl₂/MAO, and (n‐BuCp)₂ZrCl₂/MAO. Long‐chain branching in the polyethenes, as measured by dynamic rheometry, depended heavily on the catalyst and polymerization conditions. In a semibatch flow reactor, the level of branching in the polyethenes produced with Et[Ind]₂ZrCl₂/MAO increased as the ethene concentration decreased or the polymerization time increased. The introduction of hydrogen or comonomer suppressed branching. Under similar polymerization conditions, the two other catalyst systems, (n‐BuCp)₂ZrCl₂/MAO and Et[IndH₄]₂ZrCl₂/MAO, produced linear or only slightly branched polyethene. On the basis of an end‐group analysis by FTIR and molecular weight analysis by GPC, we concluded that a chain transfer to ethene was the prevailing termination mechanism with Et[Ind]₂ZrCl₂/MAO at 80 °C in toluene. For the other catalyst systems, β‐H elimination dominated at low ethene concentrations. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 376–388, 2000     

Synthesis and characterization of multiarm star-branched polyisobutylenes: Effect of arm molecular weight

A series of star-branched polyisobutylenes with varying arm molecular weights was synthesized using the 2-chloro-2,4,4-trimethylpentane/TiCl₄/pyridine initiating system and divinylbenzene (DVB) as a core-forming comonomer (linking agent). The resulting star-branched polymers were characterized with regard to the weight-average number of arms per star molecule (N̄_w) and dilute solution viscosity behavior. As the molecular weight of the arm (M̄_{w, arm}) was increased, dramatically longer star-forming reaction times were needed to produce fully developed star polymers. It was calculated that N̄_w varied from 50 to 5 as the M̄_{w, arm} was increased from 13,000 to 54,000 g/mol. The radius of gyration, R_g, of the star polymers was observed to increase as M̄_{w, arm} was increased. The solution properties of the star polymers were evaluated in heptane using dilute solution viscometry. It was determined that the stars had a much higher [η] compared to the respective linear PIB arms, but a much lower [η] compared to a hypothetical linear analog of an equivalent molecular weight. The dependence of [η] on temperature for the stars and linear arms was very small over the temperature range 25 to 75°C, with only a very slight decrease with increasing temperature. [η]_star was also determined to increase with increasing M̄_{w, arm}, but decrease with increasing M̄_{w, star}. The branching coefficient, g′, calculated for the stars at 25°C, increased as N̄_w decreased and agre ed well with literature values for other star polymer systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3767–3778, 1997     

Universal calibration in GPC: A study of polystyrene,poly-α-methylstyrene,and polypropylene

The theoretical justification for using M[_η], or a similar quantity, as a universal calibration parameter in GPC is reviewed. The equation based on this parameter is applied to transform the primary calibration curve, obtained by means of polystyrene samples, into calibration curves for poly-α-methylstyrene, polypropylene, and linear polyethylene. The Mark–Houwink equations for these polymers, as they are used in the transformation, are discussed. The resulting GPC calibration curves are compared with molecular weights and peak elution volumes of fractionated poly-α-methylstyrene and polypropylene. The same comparison is made with samples of polypropylene and polyethylene having very broad molecular weight distributions. The agreement lies within experimental error.     

The Regioselective Methylation of Polycyclic Aromatic Hydrocarbons through Tricarbonylchromium Coordination

Deprotonation, methylation, and air oxidation of polycyclic arenes coordinated to chromium(0), (η⁶-arene)Cr(CO)₃, produced ring-methylated products with high selectivity and in good yield. This procedure gave 3-methylbenz[a]anthracene from (η⁶-benz[a]anthracene)Cr(CO)₃, 3-methylphenanthrene from (η⁶-phenanthrene)Cr(CO)₃, 2-acetyl-6-methylphenanthrene from (η^6?2-acetylphenanthrene)Cr(CO)₃, and 3,7,12-trimethylbenz[a]anthracene from (η^6?7,12-dimethylbenz[a]anthracene)Cr(CO)₃.